So, what i would do if I were handed the keys and told to do whatever I wanted: Cinderella Girl election/Stage for Cinderella but make it Paradox Live.

(If you're not familiar, and I assume you as the asker are not, but also for anyone else who's reading: the thing with The Idolm@ster Cinderella Girls is that there are approaching 200 characters -- some of whom don't have voice actresses yet -- and there's an annual popularity vote that affects various things. Girls who don't have voice actresses yet can have them added if they rank high enough in these elections, since they have to be given a voice actress to participate in the group song. Note that I'm simplifying this a lot!)

So, in other words, how I would do it is:
I would throw a bunch of character concepts at the wall, and let popularity vote sort out which ones actually end up mattering. This could be through a mobile game as with Deresute, or it could just be a general voting campaign; it'd certainly be a good way to use up dope points after BoU or the like.
It wouldn't have to be as intense as Deresute's 190 characters; just think like, five potential aspiring units and whichever one wins a voting campaign gets an invite to the next Paradox Live.

This is kind of what I would do with a mobile game, mostly because I don't want a bunch of core content for the cast we already know + care about to be locked behind a mobile game (since mobile games are ephemeral and inherently have a time limit, are horrible for archival, and frankly just create horrible incentives for the structure and writing), and I think having the focus be on new characters while still being able to influence the main canon through that kind of 'graduation' would be easier to swallow (and wouldn't shut out fans of the losing groups quite as hard, lol), but honestly I could see something like that happening just straightforwardly via Paratora, etc.

In terms of group concepts, I don't really have any off the top of my head! There are certainly subgenres of hiphop they've yet to cover, and popular (or, more realistically, "unpopular but dear to my heart", lol) character tropes that haven't been implemented yet... but I'm also a Touken Ranbu fan and "oh, yeah, we don't have a character like that yet, do we???" is a constant refrain every single time we get a new sword implemented, and TKRB is coming up on 10 years, so there's always things that are super obviously "oh, huh, yeah, we didn't have that yet" in retrospect.